Many times I heard about papers published in conference. But still I am not able to find the major difference between papers published in a conference and those published in a journal. What is the difference?
Conference papers refer to articles that are written with the goal of being accepted to a conference: typically an annual (or biannual) venue with a specific scope where you can present your results to the community, usually as an oral presentation, a poster presentation, or a tabled discussion. The review process for conference papers is typically within a fixed window: everyone submits for a certain deadline, then the review committee (program committee) collaborates to review and discuss papers, then all authors are notified with accept/reject at the same time. Since the review process has a fixed schedule (to meet the schedule of the physical meeting), conference review times are quite predictable.
Conference papers are typically published in collections called "proceedings": sometimes these are printed by university presses, by professional organizations, by big-name publishers, or simply online.
Journal papers refer to an article that's published in an issue of the journal. The frequency of issues for different journals varies from one-a-month to once-a-year, or anything in between; it may not even be regular. The review process for journals often does not have a fixed deadline or schedule: though journals may promise things like "reviews in six weeks", in my experience, this rarely if ever holds true. However, instead of conferences that typically have only accept/reject decisions, journals typically have a rolling review schedule and reviewers can opt to ask the authors for revisions, meaning that there might be multiple review phases (often limited to three, at which stage the paper is rejected/accepted).
Since conference papers have a fixed schedule and provide the authors a venue for discussion and feedback, they are generally for earlier-term work or for "announcing/marking an idea", or for finding collaborators. Furthermore, conference papers tend to have fixed page-limits, which restricts the content to preliminary findings.
Journal papers tend to have generous page-limits (or none at all), but typically require the work to be more comprehensive and self-contained in return.
In general, in most fields, papers in well-recognized journals tend to have more prestige than papers in well-recognized conferences (esp. in terms of metrics). But this is a simplification.
While in some fields, conference papers are akin to talk abstracts, in areas like computer science, conference papers can be very meaty and there is a high churn of papers in conferences. Top conferences can have acceptance rates around 10%, and as such, A+ conference papers are often held in high regard within the community: these venues are far more competitive than many of the best journals. Still, even in the CS area, metric-wise (for hiring, positions, funding, etc.), journals will often still count for more than a conference following the norm in other academic fields.
It may be useful to expand on something which is implicit in Pete's answer. In pure mathematics, "conference papers" as described by badroit don't actually exist. Some (but by no means all, or even most) math conferences have published "proceedings", but these are not collections of the talks (or posters, or whatever) given at the conference. Likewise, in math there is no review process prior to the conference to decide which presentations will be given.
Instead, it is decided to have a conference, a bunch of people are invited, and some subset of them are asked to give talks. (How all of that happens varies a lot from case to case, but that's an answer for another question.) The point is that the speakers are chosen before anyone knows what they intend to talk about. The talks themselves may be about work in progress, work that's already submitted or published, or a synthesis. Basically, speakers give the same sort of talk they'd give in a departmental seminar which happened to have an audience full of experts. In particular, a talk frequently doesn't correspond to a single paper, or to work which is still available to be submitted for publication. Thus the phrase "present a paper", which people from many other fields use to describe what they do at a conference, sounds rather odd to mathematicians. (At least, it does to me.)
Finally, when there is a proceedings volume, all of the speakers — and possibly also the other participants who didn't give talks — are invited to submit papers. Those papers don't necessarily have anything to do with the actual talks (although hopefully both have to do with the topic of the conference). So the "proceedings" don't necessarily bear any resemblance to what actually happened at the conference, making "proceedings" rather a misnomer. Basically, a proceedings volume is like a one-issue journal (sometimes it is an issue of a regular journal) on the topic of the conference. Pete already explained some of the ways they are perceived differently from regular journals.
For many questions like this, you can get some kind of answer without including information on your own discipline, but it will be at best some kind of weighted average across different disciplines. If you indicate your discipline in the question then you may well get both general questions and questions focused to your discipline.
You ask about mathematics. We do not have a very strong tradition of conference papers at all compared to most other academic fields. The idea of a "prestigious conference paper" is almost an oxymoron to me. There are a small number of yearly conferences which regularly publish their proceedings, but that the papers are solid and interesting and sufficiently thematically connected to one another that you might actually want to own the book they get published in is close to a best case scenario. Actually I get annoyed even by this because conference proceedings that get published as books tend to be books which are very expensive, difficult to locate (by virtue of bibliographic information handled in a strange way) and often not carried by university libraries.
At the moment I have 22 published papers and half a dozen other submissions, and I have never submitted a paper to a conference. Curious as to whether this was my own idiosyncrasy, I just looked up the published papers of my two senior colleagues in my field (number theory). One of them has no conference papers. The other has three but the most recent is from 1989. I do get the sense that this was a more common phenomenon about a generation ago.
Why don't mathematicians like to publish conference papers? Here are some ideas:
1) I don't get the sense that many people are getting their submissions to conference proceedings turned away: rather, I think most often they simply ask everyone who spoke in the conference [or in the section, or whatever] whether they would like to contribute an article. They usually are "refereed" in some formal sense, but in my understanding it is usually nominal, and the proceedings are viewed mostly as a record of as many of the actual talks as they could persuade people to write up.
2) Because they generally do want a paper from as many people who gave a talk at the conference as possible, the shoe is really on the other foot and they often end up having to cajole busy people to get around to polishing their lecture notes. Thus unlike in other fields where I gather conference proceedings get novel work out quickly, in mathematics the proceedings can appear two years or more after the conference, which is slow even compared to journal publication.
3) There seems to be a sense that conferences (with certain obvious exceptions like the ICM) are more social occasions than serious professional events. (I mean, if I want to hear about the crackerjack theorem you proved last week, it's likely I can just download it from the arxiv or your webpage or ask you to send me a copy.) The number one reason mathematicians like to give conferences is to celebrate someone's birthday, and a popular followup is to train young people in the field: these are often called "summer schools". There is a sort of community awareness that -- again, with certain famous and not so recent exceptions like the Grothendieck Festschrift -- such conference proceedings are more likely to contain heartfelt remarks about one's revered former advisor than really cutting edge research. I have even heard some people jokingly refer to Festschrifts as dumping grounds for inferior product.